Abstract Interpretation
In the survey [1]}, linear approximation technique is contained in abstract interpretation domain [2]}, [3]}, [4]}. The over-appriximation zone is called as abstract domain in this field. In the survey [5]}, these two technique are divided. The similarity between abstract interpretation and linear approximation is that they both need to give a pair of upper and lower linear constraints of a non-linear function \(f(x)\)  in a given interval \([l,u]\) . When the abstract domain of abstract interpretation is polyhedra [6]}, there is no essential difference between these two techniques. However, when the abstract domain is zonotope [2]}, [4]}, abstract interpretation can abandon the backsubstitution process [6]} and computes faster than the linear approximation method. However, abstract interpretation has some precision loss due to its parallel linear constraints compared to linear approximation.
